some sort of dashboard with monitoring and statuses of all my services

See if Uptime Kuma suits your needs.

Are there any major no-no things a newbie might do with Docker/selfhosting that I should avoid?

Allow password based SSH authentication, you should look into key based authentication

I wanted to have it behind a domain, how would I achieve it?

Use a reverse proxy (like caddy) which serves different content based on domain name.

https://netboot.xyz/

You might not need it but it’s a very small image (3.5MB for multi-arch iso) so why not?

Serverhunter is a search engine for cloud servers and has easy to use filter functions.

I am surprised that I didn’t see anyone link to https://lowendtalk.com/ and https://lowendspirit.com/, OP can ask in both places and see what people have for offer.